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Forcing an email when a user does not want to give it just yet is a bad idea. Show them why your product is worth it first and then ask for an email or contact information.

Most likely all you will get is fake email addresses anyway causing you to waste time and resources on something that is not a valid lead.

I work for an IT firm, and I end up giving tons of sites an email to use trials, but I dislike doing so just to see a demo. For me, I prefer demos to give me an option to contact the company at the end of the demo, but I realize that this may not be terribly helpful to you as I'm not likely to contact you if the demo turned me off for some reason.

I would maybe give a place to enter your email address before the demo starts, but make it optional. You could also put a short survey at the end of the demo for feedback. I'm actually fairly likely to fill out a (very) short survey, especially if I didn't like something. The way I see it, I don't want to really risk being inundated with unwanted email from a company, but I'm willing to give my opinion and add an email contact if I think it will be used for improving the product rather than to try advertising to me.

Which ones? Three of them involve giving you stuff for free. How can you not like that?